
On \(C([0,T];A)\)  (or \(D([0,T];A)\) ), \(\operatorname{d}_C\)  denotes the metric corresponding to the supremum-norm, denoted by \(\Vert  \cdot \Vert \) . Whenever the context is clear, we write \(\operatorname{d}:=\operatorname{d}_C\) . On \(D([0,T];A)\)  we denote by \(\operatorname{d}_D\)  the metric given, e.g., in [1]}, Sections 12.1 and 12.2 which defines the Skorohod topology in such a way that the resulting space is Polish. The resulting metric spaces are denoted by \(C([0,T];A;\operatorname{d}_C)\) , \(D([0,T];A;\operatorname{d}_C)\)  and \(D([0,T];A;\operatorname{d}_D)\) , respectively (where the metrics are omitted, whenever they are clear from the context).
